Make dough and refrigerate until ready to use.
Preheat the oven to 400 degrees F.
In a large Dutch oven or sauce pan, heat the olive oil over medium-high heat. Sauté the onion, carrots, and celery in the pan until soft, but not brown. (About 5 minutes.) Season to taste with salt and pepper.
While the vegetables are softening, shred the cooked chicken. Leftover chicken or a store-bought rotisserie chicken is excellent in this recipe. Set the shredded chicken aside in a large bowl.
Use a slotted spoon to remove vegetables from the pan, placing them in the bowl with the shredded chicken; set aside.
Heat the butter in the now empty Dutch (still over medium-high heat.) The butter will foam as it melts. Once the foaming stops, whisk in the flour. Cook the flour/butter for one minute…whisking constantly.
Pour in the milk and chicken stock. Continue to whisk until smooth. Add the thyme.
Reduce heat to medium-low, and simmer until sauce fully thickens, stirring constantly. (About 1-2 minutes.)
Taste sauce and adjust salt & pepper, to taste.
Pour sauce over chicken and vegetables in the large bowl; stir to combine. (Can be cooled, covered, and reheated overnight. Re-warm filling before filling pie.)
Stir in the peas. Set filling aside while rolling out pie dough. (If refrigerated, allow pie to to “warm” on the counter for 10 minutes before rolling out.)
Roll half of the No Excuses Pie Dough on a lightly floured surface into a circle, 12-inches in diameter. (Or use refrigerated, rolled pie crust—you may need to roll it a bit larger.)
Gently roll the dough/pastry around the rolling pin to transfer to a 10-inch pie plate.
Check that dough is fully touching the bottom and sides of the pie plate.
Spoon the warm filling into the pastry lined pie plate.
Roll the other half of the No Excuses Pie Dough into a 12-inch circle. Roll the circle around the rolling pin, and transfer it to cover the top of the filled pie.
Trim the edges of the pastry, and then fold & crimp the edges.
Cut vent slits in the top of the pie. Brush top with egg wash, if desired.
Bake until crust is fully cooked, top and bottom, and a deep golden brown; about 35-40 minutes. (If edges become too dark, cover with aluminum foil and continue baking until pie is done.)
Let pie rest for 10 minutes before serving.